What are savory or sweet dishes of beaten egg cooked in fat?

You're describing a dish that falls under the broad umbrella of eggs cooked in fat, and there's a delicious world of possibilities! Here are some examples, broken down by savory and sweet:

Savory:

* Scrambled Eggs: Probably the most basic, yet infinitely customizable. You can add cheese, veggies, meat, spices, and more.

* Omelets: A thin, folded egg dish that can be stuffed with a variety of fillings, from cheese and ham to mushrooms and spinach.

* Frittatas: Similar to an omelet, but often thicker and baked in the oven, allowing for a wider variety of ingredients.

* Eggs Benedict: A classic brunch dish featuring poached eggs on English muffins, topped with hollandaise sauce and ham or smoked salmon.

* Shakshuka: A North African and Middle Eastern dish of eggs poached in a tomato-based sauce with spices and often vegetables.

* Eggs Florentine: A lighter version of Eggs Benedict, using spinach instead of ham.

* Quiche: A savory tart with a pastry crust and a filling of eggs, cheese, and other ingredients.

* Pão de Queijo: Brazilian cheese bread made with tapioca starch, eggs, and cheese, often fried in oil.

Sweet:

* French Toast: Thick slices of bread soaked in a mixture of eggs, milk, and often spices, then fried.

* Dutch Baby (or German Pancake): A puffy, pancake-like dish cooked in a hot skillet, often served with fruit and powdered sugar.

* Crepes: Thin, delicate pancakes made with eggs, flour, and milk, often filled with sweet or savory ingredients.

* Flan: A custard dessert, often made with eggs, milk, and sugar, and baked in a water bath.

* Crème brûlée: A rich custard dessert with a caramelized sugar topping.

This is just a starting point! Within each category, there are countless regional and cultural variations. Let me know if you want to explore any of these dishes in more detail, or if you have a specific type of cuisine in mind. 😊